SAT Mastering Order of Operations: PEMDAS Accuracy Under Pressure

PEMDAS provides a strict hierarchy for operations. Multiplication and division have equal priority and are evaluated left to right, as are addition and subtraction. This equal-priority rule trips students who think all multiplication happens before division.

Parentheses, including brackets and fraction bars, create new "mini-expressions" that must be evaluated first. Exponents apply only to the term they modify, not to an entire expression unless parentheses explicitly include it.

Before computing, identify all operations and their priority levels. Mark parentheses and fraction bars to clarify grouping, then evaluate step by step from highest to lowest priority. This deliberate annotation prevents the rushing that causes errors.

Check 1: Parentheses and grouping symbols; Check 2: Exponents; Check 3: Multiplication and division left-to-right, then addition and subtraction left-to-right.

Example 1: 2+3×4=? Students compute 5×4=20 (wrong) instead of 2+12=14. Example 2: 2^3^2=? Is it (2^3)^2=64 or 2^(3^2)=512? (Exponents are right-associative, so 512.) Example 3: 12/2×3=? Compute left-to-right: 6×3=18, not 12/6=2.

Example 4: -3^2=? The negative is not squared; only the 3 is. Result is -9, not 9. Example 5: (2+3)^2=5^2=25, not 2+3^2=2+9=11.

Solve three PEMDAS problems daily, alternating between problems with parentheses, exponents, and mixed operations. Time yourself: each problem should take under 30 seconds once you build automaticity. Use your three-check verification on all problems until checking becomes automatic.

Day 1: Three problems with parentheses. Day 2: Three with exponents. Day 3: Three with mixed operations. Repeat and gradually reduce time.